Understanding the adsorption and growth mechanisms of large π -conjugated molecules on noble metal surfaces is a crucial aspect for designing and optimizing electronic devices based on organic materials. The investigation of adsorption heights for these molecules on different surfaces can be a direct measure for the strength of the adsorbate-substrate interaction, and gives insight into the fundamental bonding mechanisms. However, the adsorption strength is often also influenced by intermolecular (lateral) interactions which cause, e.g., island formation in the submonolayer regime and influence the adsorption geometry of individual molecules. The lateral structure can then dominate the vertical structure formation and influence the adsorbate-substrate interaction. In this context, the adsorption of copper-phthalocyanines on noble metal surfaces [Au(111), Ag(111), and Cu (111)] represents an ideal model system since the lateral structure formation, as well as the molecular adsorption geometries, strongly depend on coverage and temperature, and hence can be tuned easily. We demonstrate that for CuPc/Au(111), a system dominated by physisorption, the adsorption height of the molecules is independent from the lateral adsorption geometry. In contrast, a strong chemisorption of CuPc on Cu(111) shows a clear gradient in the interaction strength: Individual molecules in diluted phases are significantly stronger bonded than molecules in dense phases. This finding quantifies the increase of the exchange correlation in the binding process, which goes along with the tendency to a more site-specific adsorption geometry at small coverages.